In this section, we focus on the comparison of the modeled Hapke parameters of asteroids Lutetia and Steins with results from laboratory samples (terrestrial and extra terrestrial).
Since the imperfection of Hapke model do not allow to interpret the physical meaning of Hapke parameters, it is self-evident that we do not expect from the photometry of mete-orite to determine the meteoritic analog of asteroid. Instead we can deduce whether the light scattering behavior consistency exists between the regolith on Lutetia and the avail-able laboratory samples. In other words, this comparison helps to constrain the albedo and the grain size of regolith covering the surface of Lutetia. The taxonomic type and min-eralogical composition of Lutetia is not established yet. However, Vernazza et al. (2011) proposed enstatite chondrite meteorite for Lutetia, based on the visible, mid-infrared and near-infrared telescopic spectra. As mentioned in chapter 5, VIRITS measurements from the northern hemisphere of Lutetia also suggest two different types of meteorites, ei-ther metal-rich carbonaceous chondrite or enstatite chondrite meteorites (Coradini et al., 2011). The ground-based spectra and radar measurements also suggest a similar com-position for Lutetia and the possible analogy with CO/CV meteorites (Belskaya et al., 2010).
Among the available Hapke parameters retrieved for a number of soil and meteorite samples in the literature such as Olivine S, Olivine L, and Red Clay in Shkuratov et al.
(2012), three types of basalt materials in Cord et al. (2003), 14 samples with the discrete physical properties in Shepard and Helfenstein (2007) and 8 meteorite samples being contemplated as asteroid regolith in Beck et al. (2012), we found two samples that they match with the reflectance measurement of Lutetia.
The first best-fit sample is the packed state of "Chromium Oxide" (CRp) at λ=450 nm, examined by Shepard and Helfenstein (2007). CRp contains very fine particles (≤1 µm) which have a tendency to form into larger unit such as aggregate of up to 1 mm size (Figure 6.6). The modeled Hapke parameters of CRp are: SSA=0.45, B0=0.95, h=0.05, b=0.37, c=-0.58 andθ=13◦(Shepard and Helfenstein, 2007).
In Figure 6.7a, the disk-integrated phase function of Lutetia from WAC F17 (631.6 nm) and NAC F22 & F82 images (649.2 nm) is plotted together with the phase function of CRp sample atλ=450 nm (CRp 450) based on its modeled Hapke parameters and in Figure 6.7b, the disk-resolved data of Lutetia in the phase angle range of 3◦ to 63◦ are compared with modeled I/F of CRp 450 sample. The scatter-plot in Figure 6.7b with a linear correlation coefficient of 0.93 indicate a fairly good fit, however clear systematic deviation is seen for the high I/F values which are link to the images at α < 10◦. This 118
6.3 Comparison with laboratory measurements
(a) (b) (c)
Figure 6.6: Panel (a) and Panel (b) show the optical images of Chromium oxide sam-ple (CR) in the loose (CRl) and packed (CRp) states, respectively. Panel (c) shows the scanning electron microscope image of CR. Figure is taken from Shepard and Helfenstein (2007).
similarity suggests a layer of concrete material as regolith on Lutetia.
Considering Spjuth et al. (2012)’s finding that there is a link between chromium oxide sample in loose state (CRl sample) with disk-resolved reflectance measurement of aster-oid Steins. CRp and CRl samples are similar in mean grain size but differ in bulk porosity (see Figure 6.6). The bulk porosity of CRp and CRl samples are calculated to be 71% and 84%, as reported by Shepard and Helfenstein (2007). This indicates that the regolith on the surface of Lutetia is less porous than Steins. The porosity distinction also appeared in the width of opposition effect h of Lutetia (h=0.050±0.003) and Steins (h=0.024±0.002).
Considering the relation between h and porosity as described in chapter 2, the higher h for Lutetia suggests lower porosity p on its surface in comparison to Steins.
The second one is "Allende" meteorite. Allende belongs to the CV3 carbonaceous chondrites. This sample is analyzed by Beck et al. (2012) in such a form that resemble the surface of asteroids (see Figure 6.9). The analysis reported the average grain size of roughly higher than 150 µm, which is distributed uniformly. The Hapke parameters of Allende sample derived from Beck et al. (2012)’s experiment are: SSA=0.357, B0=1.00, h=0.063, b=0.259, c=-0.067,θ=3.59◦.
The measurements are given by Beck et al. (2012) in reflectance factor (RF) unit, which differ from the radiance factor by cosine of the incidence angle (µ0). Therefore, we can only compared the disk-resolved data of Lutetia with their reflectance measurement adjustingµ0 based on the shape model of Lutetia.
Considering the µ0 correction, Figure 6.10 displays the scatter plot of the modeled reflectance factor from the Hapke parameters versus the measured reflectance factor of Lutetia with a reasonably good linear correlation coefficient of 0.91. The laboratory mea-surement is limited to the lowest phase angle range of 3◦and the amplitude of opposition effect B0is fixed to 1. For this reason, we do not include the measured data of Lutetia for α <3◦, however, we still have points deviated from the linear fit in Figure 6.10 because of data from images at small phase angles (opposition surge range 0◦ to 10◦).
The similarity of reflectance factor measurements between the Allende meteorite
6 Comparison of Asteroids Steins and Lutetia with other small bodies
0 50 100 150
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Phase Angle (deg)
I/F
Lutetia CRp 450
(a)
0 0.05 0.1 0.15 0.2
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
Measured I/F (Lutetia)
Modeled I/F (CRp 450)
(b)
Figure 6.7: Comparison of disk-integrated and disk-resolved data of Lutetia atλ=631.6 nm and 649.2 nm with those modeled by applying Hapke parameters of the packed chromium oxide sample (CRp) in panel (a) and panel (b), respectively (Masoumzadeh et al., 2015).
120
6.3 Comparison with laboratory measurements (λ=650 nm) and Lutetia at λ=649.2 nm probably has two relevant aspects. First, the presence of carbonaceous chondrite, like Allende, is expected in the surface of Lutetia as discussed in chapter 5, especially based on the emissivity spectra of Lutetia studied by Barucci et al. (2008). The multicolor reflectance spectrum of the Allende meteorite sample obtained by Grisolle et al. (2011), displays a fairly flat reddening slope in the wavelength range of 0.4µm to 1.2µm and it shows the average reflectance is 8 % brighter compared to the two other carbonaceous chondrites, Orgueil and Taglish lake used by Beck et al. (2012) in the laboratory study (Figure 6.8). Therefore, regarding the moderate albedo and the flat spectral shape of the disk-average brightness of Lutetia from OSIRIS data, we can deduce from measured reflectance that the surface of Lutetia might resemble Allende meteorite material.
Figure 6.8: Reflectance spectra of 3 carbonaceous chondrite(CC) meteorites powders:
Tagish Lake(ungrouped CC) , Orgueil(CI) and Allende(CV3) studied by Beck et al.
(2012) in the spectral range of 0.4µm to 1.2 µm. All spectra obtained by Grisolle et al.
(2011) atα=30◦.
Secondly it is noted that the grain dimension of Allende sample (>150 µm) and the grain size estimated by VIRTIS (Coradini et al., 2011) for the surface of Lutetia (2.1±3.41.7× 102µm) are consistent with each other. This consistency can tell us the potential role of mechanical properties in the similarity of reflectance values.
A two-parameter b and c of the particle phase function, known as a double-term Henyey-Greenstein (2HG) phase function, described in chapter 2, can also provide gen-eral information about the properties of particles such as angular scattering, type and size of the particles. It is possible to derive the values of particle phase function parameters b and c from the disk-integrated phase function of Lutetia since it extends to large phase an-gles. The b and c parameters represent the forward and backward lobes of scattered light from a particle. Based on the experimental study of McGuire and Hapke (1995) for three artificial types (glass, metal and polyester resin) of spherical and irregular particles with different roughness, the modeled parameters of Lutetia b=0.33 and c=0.095 are located in the middle of the 2HG parameters diagram (Figure 6.11). This means the regolith on Lutetia is best comparable with rough and relatively spherical resin particles. The posi-tive value of c also implies that particles on the surface of Lutetia are well back scattering with a small forward scattered lobe. In fact, the density of internal scatterers controls the
6 Comparison of Asteroids Steins and Lutetia with other small bodies
Figure 6.9: Optical microscope images of Allende powder sample from Beck et al. (2012).
0 0.1 0.2 0.3 0.4 0.5
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Measured reflectance (Lutetia)
Modeled reflectance (Allende)
Figure 6.10: Comparison of disk-resolved data of Lutetia from NAC F82 & F22 images atλ=649.2 nm with those modeled by Hapke parameters of the Allende meteorite sample based on Beck et al. (2012)’s laboratory analysis through a filter with the central wave-length of 650 nm (Masoumzadeh et al., 2015).
122
6.3 Comparison with laboratory measurements forward and backward scattering lobes. Thus, the density of internal scatterers for Lutetia is relatively moderate.
Figure 6.11 also displays the position of Steins in the 2HG parameters diagram. In comparison with Lutetia, the regolith on Steins may contain internal scatterers in large quantities (as discussed in Spjuth et al. (2012)) and it is rougher than Lutetia.
Cord et al. (2003) also conducted an experiment to constrain the two-parameter of 2HG phase function for three samples in four grain sizes (all less than 3 mm) which are analogues to the planetary regolith such as fresh basalt, altered basalt and oxidized basalt materials. Based on their findings, the resulting b values fall into the range of 0.4 to 0.5 and the c values vary between 0.13 to 0.56 for the all breeds. This suggests that the behavior of Lutetia’s parameters b and c are very different from that of basaltic materials.
Figure 6.11: The position of asteroids Steins (blue circle) and Lutetia (red circle) in the 2HG parameters plot. The 2HG parameters diagram is taken from McGuire and Hapke (1995).
7 Conclusions
Finally, in this chapter I gave a brief statement about what I have done and what I have concluded in the context of light scattering properties for two asteroids Steins and Lutetia and compared to other small bodies.
I applied two photometric functions of Minnaert and Hapke, for both asteroids Steins and Lutetia using OSIRIS measurements. I employed a direct search which is called Nelder-Mead simplex, to obtain optimal values of photometric parameters. I used the images from both OSIRIS cameras, NAC data in the wavelength range of 269.3 nm to 989.3 nm and WAC data withλbetween 295.9 nm to 631.6 nm. I constructed the disk-integrated phase function of both asteroids in different filters. Those atλ=631.4 and 649.2 nm are the most complete ones due to the wide phase angle coverage.
I developed a tool to extract disk-resolved intensity and the corresponding geometric angles per facet from observed images, using the shape models. In order to validate my approach, I utilized the WAC images of Steins and compared my findings with the work done by Spjuth et al. (2012). The comparison indicates good agreement and it confirms the reliability of my technique.
The Minnaert modeling describes the light scattering properties of Lutetia’s surface satisfactory well for phase angles<80◦, whereas for Steins, it represents a good fit until α=20◦. For Lutetia, the modeled Minnaert k parameter at opposition (k0=0.526±0.002) indicates a flat distribution in the surface brightness. No wavelength dependence is found for the k value of Lutetia. The k value of Steins, evaluated only for the phase angle dependence, is equal to 0.589±0.004 at zero phase angle, suggesting a limb-darkened disk for the body.
I also modeled the Hapke parameters for Steins through nine filters of the WAC cam-era and compare my results with those of Spjuth et al. (2012). The Hapke modeling of Steins atλ=631.6 nm yields a high single scattering albedo (SSA=0.618±0.002) and very low amplitude of the shadow-hiding opposition surge (B0=0.70±0.02). The width of op-position surge is 0.024±0.002. The asymmetry factor g is estimated to be -0.313±0.003.
The roughness parameterθis contained to be 27◦±1◦, which is a typical value for aster-oids and agrees with the one retrieved by Spjuth et al. (2012).
Multi-wavelength values of Hapke parameters are also evaluated for Lutetia through WAC and NAC images. The SSA spectrum displays a relatively flat slope in agreement with Lutetia’s spectrum as measured by VIRTIS spectrometer on-board Rosetta (Coradini et al., 2011). The best-fit value Hapke parameters of Lutetia atλ=631.6 nm and 649.2 nm are as follows; The SSA is 0.226±0.002. The opposition surge parameters B0is 1.79±0.08 and h is 0.050±0.003. The g-parameter of the particle phase function p(α) is estimated to be -0.28±0.01. The roughness value θis calculated to be 28◦±1◦ in the case of NAC F82 & F22 (649.2 nm) images and 24◦±1◦ for the WAC F17 (631.6 nm) images. The
7 Conclusions
value of 24◦ is consistent with the one retrieved from VIRITS data to be 23.6◦ (Andrea Raponi, personal communication). Indeed, the spatial resolution of VIRTIS-M hyper-spectral images is different from that of OSIRIS-NAC, but similar to OSIRIS-WAC, which may have resulted in different and similar roughness parameters, respectively. I noticed that in the collection of small bodies, the Hapke parameters of Lutetia are similar to those of S-type asteroids, with a rather higher opposition surge amplitude and width.
The overall light scattering variation across the surface of Lutetia is investigated by generating the albedo ratio maps, phase ratio maps and color ratio maps. The albedo variation on Lutetia is around 10% as found from albedo ratio maps of NAC F82 &
F22 (649.2 nm) images at small phase angles (α <30◦). The phase ratio maps display only small variations over the surface which may be caused by phase function or/and the photometric roughness alteration. This is confirmed by the corresponding simulated phase ratio maps. No large scale variation across the surface are found in the color ratio maps of (805.3nm/535.7 nm) and (701.2nm/535.5nm). However, it is found that Lutetia’s surface shows subtle variations in color of the order of 10% based on the color ratio map of (931.9nm/269.3 nm). It is worthy of note that the overall photometric variations of Lutetia across the surface is very similar to Mathilde (C-type asteroid) and Steins (E-type steroid).
I conduct the comparison between the Lutetia results and available laboratory flectance measurement. Close similarity of Lutetia’s light scattering behavior with re-flectance measurements of two samples are found i.e. with Chromium oxide in the packed state (Shepard and Helfenstein, 2007) and with an Allende meteorite sample (Beck et al., 2012). I conclude that the similarity of photometric parameters of Lutetia with the packed chromium oxide shows that the regolith on Lutetia is dense and concrete. Lutetia’s surface is also less spongy, in comparison with Steins which seems to be similar to Chromium oxide in loose state (Spjuth et al., 2012).
The consistency of Allende meteorite sample with Lutetia might indicate a similarity in the overall material constitution or at least for the size distribution to contain 150µm and larger grains. The mean grain size of Lutetia’s regolith is calculated by VIRITIS measurement (Coradini et al., 2011) to be (2.1±3.41.7×102µm). Note that among available meteorite sample analyzed in the laboratory in the context of bidirectional measurement, what I found about the consistency of Allende meteorite sample (belong to subgroup CV3 of carbonaceous chondrties) and Lutetia, it does not contradict what I said about the similarity of the modeled Hapke parameters of Lutetia with average S-type asteroids because neither of them is aimed to find an analog for Lutetia. As argued in Helfenstein and Veverka (1989), the main difference between the Hapke parameters of C-type and S-type asteroids are for the SSA, not for other Hapke parameters. Therefore, since the Allende meteorite has a rather moderate albedo compared to other carbonaceous chondrtie meteorites, it resembles the Lutetia reflectance data.
126
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